Search results for: partial differential equation
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4221

Search results for: partial differential equation

3801 An Analytical Method for Bending Rectangular Plates with All Edges Clamped Supported

Authors: Yang Zhong, Heng Liu

Abstract:

The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

Procedia PDF Downloads 587
3800 The Prediction of Effective Equation on Drivers' Behavioral Characteristics of Lane Changing

Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

Abstract:

According to the increasing volume of traffic, lane changing plays a crucial role in traffic flow. Lane changing in traffic depends on several factors including road geometrical design, speed, drivers’ behavioral characteristics, etc. A great deal of research has been carried out regarding these fields. Despite of the other significant factors, the drivers’ behavioral characteristics of lane changing has been emphasized in this paper. This paper has predicted the effective equation based on personal characteristics of lane changing by regression models.

Keywords: effective equation, lane changing, drivers’ behavioral characteristics, regression models

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3799 Assessing Influence of End-Boundary Conditions on Stability and Second-Order Lateral Stiffness of Beam-Column Elements Embedded in Non-Homogeneous Soil

Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

Abstract:

This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

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3798 Using Scilab® as New Introductory Method in Numerical Calculations and Programming for Computational Fluid Dynamics (CFD)

Authors: Nicoly Coelho, Eduardo Vieira Vilas Boas, Paulo Orestes Formigoni

Abstract:

Faced with the remarkable developments in the various segments of modern engineering, provided by the increasing technological development, professionals of all educational areas need to overcome the difficulties generated due to the good understanding of those who are starting their academic journey. Aiming to overcome these difficulties, this article aims at an introduction to the basic study of numerical methods applied to fluid mechanics and thermodynamics, demonstrating the modeling and simulations with its substance, and a detailed explanation of the fundamental numerical solution for the use of finite difference method, using SCILAB, a free software easily accessible as it is free and can be used for any research center or university, anywhere, both in developed and developing countries. It is known that the Computational Fluid Dynamics (CFD) is a necessary tool for engineers and professionals who study fluid mechanics, however, the teaching of this area of knowledge in undergraduate programs faced some difficulties due to software costs and the degree of difficulty of mathematical problems involved in this way the matter is treated only in postgraduate courses. This work aims to bring the use of DFC low cost in teaching Transport Phenomena for graduation analyzing a small classic case of fundamental thermodynamics with Scilab® program. The study starts from the basic theory involving the equation the partial differential equation governing heat transfer problem, implies the need for mastery of students, discretization processes that include the basic principles of series expansion Taylor responsible for generating a system capable of convergence check equations using the concepts of Sassenfeld, finally coming to be solved by Gauss-Seidel method. In this work we demonstrated processes involving both simple problems solved manually, as well as the complex problems that required computer implementation, for which we use a small algorithm with less than 200 lines in Scilab® in heat transfer study of a heated plate in rectangular shape on four sides with different temperatures on either side, producing a two-dimensional transport with colored graphic simulation. With the spread of computer technology, numerous programs have emerged requiring great researcher programming skills. Thinking that this ability to program DFC is the main problem to be overcome, both by students and by researchers, we present in this article a hint of use of programs with less complex interface, thus enabling less difficulty in producing graphical modeling and simulation for DFC with an extension of the programming area of experience for undergraduates.

Keywords: numerical methods, finite difference method, heat transfer, Scilab

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3797 Differential Antibrucella Activity of Bovine and Murine Macrophages

Authors: Raheela Akhtar, Zafar Iqbal Chaudhary, Yongqun Oliver He, Muhammad Younus, Aftab Ahmad Anjum

Abstract:

Brucella abortus is an intracellular pathogen affecting macrophages. Macrophages release some components such as lysozymes (LZ), reactive oxygen species (ROS) and reactive nitrite intermediates (RNI) which are important tools against intracellular survival of Brucella. The antibrucella activity of bovine and murine macrophages was compared following stimulation with Brucella abortus lipopolysaccharides. Our results revealed that murine macrophages were ten times more potent to produce antibrucella components than bovine macrophages. The differential production of these components explained the differential Brucella killing ability of these species that was measured in terms of intramacrophagic survival of Brucella in murine and bovine macrophages.

Keywords: bovine macrophages, Brucella abortus, cell stimulation, cytokines, Murine macrophages

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3796 Free Vibration of Functionally Graded Smart Beams Based on the First Order Shear Deformation Theory

Authors: A. R. Nezamabadi, M. Veiskarami

Abstract:

This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration

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3795 A Cross-Cultural Investigation of Self-Compassion in Adolescents Across Gender

Authors: H. N. Cheung

Abstract:

Self-compassion encourages one to accept oneself, reduce self-criticism and self-judgment, and see one’s shortcomings and setbacks in a balanced view. Adolescent self-compassion is a crucial protective factor against mental illness. It is, however, affected by gender. Given the scarcity of self-compassion scales for adolescents, the current study evaluates the Self-Compassion Scale for Youth (SCS-Y) in a large cross-cultural sample and investigates how the subscales of SCS-Y relate to the dimensions of depressive symptoms across gender. Through the internet-based Qualtrics, a total of 2881 teenagers aged 12 to 18 years were recruited from Hong Kong (HK), China, and the United Kingdom. A Multiple Indicator Multiple Cause (MIMIC) model was used to evaluate measurement invariance of the SCS-Y, and differential item functioning (DIF) was checked across gender. Upon the establishment of the best model, a multigroup structural equation model (SEM) was built between factors of SCS-Y and Multidimensional depression assessment scale (MDAS) which assesses four dimensions of depressive symptoms (emotional, cognitive, somatic and interpersonal). The SCS-Y was shown to have good reliability and validity. The MIMIC model produced a good model fit for a hypothetical six-factor model (CFI = 0.980; TLI = 0.974; RMSEA = 0.038) and no item was flagged for DIF across gender. A gender difference was observed between SCS-Y factors and depression dimensions. Conclusions: The SCS-Y exhibits good psychometric characteristics, including measurement invariance across gender. The study also highlights the gender difference between self-compassion factors and depression dimensions.

Keywords: self compassion, gender, depression, structural equation modelling, MIMIC model

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3794 Exact Solutions of Discrete Sine-Gordon Equation

Authors: Chao-Qing Dai

Abstract:

Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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3793 Development of Method for Detecting Low Concentration of Organophosphate Pesticides in Vegetables Using near Infrared Spectroscopy

Authors: Atchara Sankom, Warapa Mahakarnchanakul, Ronnarit Rittiron, Tanaboon Sajjaanantakul, Thammasak Thongket

Abstract:

Vegetables are frequently contaminated with pesticides residues resulting in the most food safety concern among agricultural products. The objective of this work was to develop a method to detect the organophosphate (OP) pesticides residues in vegetables using Near Infrared (NIR) spectroscopy technique. Low concentration (ppm) of OP pesticides in vegetables were investigated. The experiment was divided into 2 sections. In the first section, Chinese kale spiked with different concentrations of chlorpyrifos pesticide residues (0.5-100 ppm) was chosen as the sample model to demonstrate the appropriate conditions of sample preparation, both for a solution or solid sample. The spiked samples were extracted with acetone. The sample extracts were applied as solution samples, while the solid samples were prepared by the dry-extract system for infrared (DESIR) technique. The DESIR technique was performed by embedding the solution sample on filter paper (GF/A) and then drying. The NIR spectra were measured with the transflectance mode over wavenumber regions of 12,500-4000 cm⁻¹. The QuEChERS method followed by gas chromatography-mass spectrometry (GC-MS) was performed as the standard method. The results from the first section showed that the DESIR technique with NIR spectroscopy demonstrated good accurate calibration result with R² of 0.93 and RMSEP of 8.23 ppm. However, in the case of solution samples, the prediction regarding the NIR-PLSR (partial least squares regression) equation showed poor performance (R² = 0.16 and RMSEP = 23.70 ppm). In the second section, the DESIR technique coupled with NIR spectroscopy was applied to the detection of OP pesticides in vegetables. Vegetables (Chinese kale, cabbage and hot chili) were spiked with OP pesticides (chlorpyrifos ethion and profenofos) at different concentrations ranging from 0.5 to 100 ppm. Solid samples were prepared (based on the DESIR technique), then samples were scanned by NIR spectrophotometer at ambient temperature (25+2°C). The NIR spectra were measured as in the first section. The NIR- PLSR showed the best calibration equation for detecting low concentrations of chlorpyrifos residues in vegetables (Chinese kale, cabbage and hot chili) according to the prediction set of R2 and RMSEP of 0.85-0.93 and 8.23-11.20 ppm, respectively. For ethion residues, the best calibration equation of NIR-PLSR showed good indexes of R² and RMSEP of 0.88-0.94 and 7.68-11.20 ppm, respectively. As well as the results for profenofos pesticide, the NIR-PLSR also showed the best calibration equation for detecting the profenofos residues in vegetables according to the good index of R² and RMSEP of 0.88-0.97 and 5.25-11.00 ppm, respectively. Moreover, the calibration equation developed in this work could rapidly predict the concentrations of OP pesticides residues (0.5-100 ppm) in vegetables, and there was no significant difference between NIR-predicted values and actual values (data from GC-MS) at a confidence interval of 95%. In this work, the proposed method using NIR spectroscopy involving the DESIR technique has proved to be an efficient method for the screening detection of OP pesticides residues at low concentrations, and thus increases the food safety potential of vegetables for domestic and export markets.

Keywords: NIR spectroscopy, organophosphate pesticide, vegetable, food safety

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3792 Fast and Accurate Finite-Difference Method Solving Multicomponent Smoluchowski Coagulation Equation

Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

Abstract:

We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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3791 Double Negative Differential Resistance Features in GaN-Based Bipolar Resonance Tunneling Diodes

Authors: Renjie Liu, Junshuai Xue, Jiajia Yao, Guanlin Wu, Zumao L, Xueyan Yang, Fang Liu, Zhuang Guo

Abstract:

Here, we report the study of the performance of AlN/GaN bipolar resonance tunneling diodes (BRTDs) using numerical simulations. The I-V characteristics of BRTDs show double negative differential resistance regions, which exhibit similar peak current density and peak-to-valley current ratio (PVCR). Investigations show that the PVCR can approach 4.6 for the first and 5.75 for the second negative resistance region. The appearance of the two negative differential resistance regions is realized by changing the collector material of conventional GaN RTD to P-doped GaN. As the bias increases, holes in the P-region and electrons in the N-region undergo resonant tunneling, respectively, resulting in two negative resistance regions. The appearance of two negative resistance regions benefits from the high AlN barrier and the precise regulation of the potential well thickness. This result shows the promise of GaN BRTDs in the development of multi-valued logic circuits.

Keywords: GaN bipolar resonant tunneling diode, double negative differential resistance regions, peak to valley current ratio, multi-valued logic

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3790 Optimization of Shale Gas Production by Advanced Hydraulic Fracturing

Authors: Fazl Ullah, Rahmat Ullah

Abstract:

This paper shows a comprehensive learning focused on the optimization of gas production in shale gas reservoirs through hydraulic fracturing. Shale gas has emerged as an important unconventional vigor resource, necessitating innovative techniques to enhance its extraction. The key objective of this study is to examine the influence of fracture parameters on reservoir productivity and formulate strategies for production optimization. A sophisticated model integrating gas flow dynamics and real stress considerations is developed for hydraulic fracturing in multi-stage shale gas reservoirs. This model encompasses distinct zones: a single-porosity medium region, a dual-porosity average region, and a hydraulic fracture region. The apparent permeability of the matrix and fracture system is modeled using principles like effective stress mechanics, porous elastic medium theory, fractal dimension evolution, and fluid transport apparatuses. The developed model is then validated using field data from the Barnett and Marcellus formations, enhancing its reliability and accuracy. By solving the partial differential equation by means of COMSOL software, the research yields valuable insights into optimal fracture parameters. The findings reveal the influence of fracture length, diversion capacity, and width on gas production. For reservoirs with higher permeability, extending hydraulic fracture lengths proves beneficial, while complex fracture geometries offer potential for low-permeability reservoirs. Overall, this study contributes to a deeper understanding of hydraulic cracking dynamics in shale gas reservoirs and provides essential guidance for optimizing gas production. The research findings are instrumental for energy industry professionals, researchers, and policymakers alike, shaping the future of sustainable energy extraction from unconventional resources.

Keywords: fluid-solid coupling, apparent permeability, shale gas reservoir, fracture property, numerical simulation

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3789 Application of Fractional Model Predictive Control to Thermal System

Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

Abstract:

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: fractional model predictive control, fractional order systems, thermal system, predictive control

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3788 Regularization of Gene Regulatory Networks Perturbed by White Noise

Authors: Ramazan I. Kadiev, Arcady Ponosov

Abstract:

Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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3787 Gender and Political Participation in Africa

Authors: Ibrahim Baba

Abstract:

The work examines the nature and causes of differential politics in Africa with particular reference to the sub-Saharan region of the continent. It also among other objectives provides alternative panacea to gender discrimination in African politics and offers solutions on how to promote political inclusion of all citizens in respect of gender differences in Africa. The work is conducted using library base documentation analysis.

Keywords: gender, political, participation, differential politics, sub-Saharan Africa

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3786 A Spectral Decomposition Method for Ordinary Differential Equation Systems with Constant or Linear Right Hand Sides

Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

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3785 Dynamic Process Monitoring of an Ammonia Synthesis Fixed-Bed Reactor

Authors: Bothinah Altaf, Gary Montague, Elaine B. Martin

Abstract:

This study involves the modeling and monitoring of an ammonia synthesis fixed-bed reactor using partial least squares (PLS) and its variants. The process exhibits complex dynamic behavior due to the presence of heat recycling and feed quench. One limitation of static PLS model in this situation is that it does not take account of the process dynamics and hence dynamic PLS was used. Although it showed, superior performance to static PLS in terms of prediction, the monitoring scheme was inappropriate hence adaptive PLS was considered. A limitation of adaptive PLS is that non-conforming observations also contribute to the model, therefore, a new adaptive approach was developed, robust adaptive dynamic PLS. This approach updates a dynamic PLS model and is robust to non-representative data. The developed methodology showed a clear improvement over existing approaches in terms of the modeling of the reactor and the detection of faults.

Keywords: ammonia synthesis fixed-bed reactor, dynamic partial least squares modeling, recursive partial least squares, robust modeling

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3784 Commutativity of Fractional Order Linear Time-Varying Systems

Authors: Salisu Ibrahim

Abstract:

The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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3783 Two-Photon-Exchange Effects in the Electromagnetic Production of Pions

Authors: Hui-Yun Cao, Hai-Qing Zhou

Abstract:

The high precision measurements and experiments play more and more important roles in particle physics and atomic physics. To analyse the precise experimental data sets, the corresponding precise and reliable theoretical calculations are necessary. Until now, the form factors of elemental constituents such as pion and proton are still attractive issues in current Quantum Chromodynamics (QCD). In this work, the two-photon-exchange (TPE) effects in ep→enπ⁺ at small -t are discussed within a hadronic model. Under the pion dominance approximation and the limit mₑ→0, the TPE contribution to the amplitude can be described by a scalar function. We calculate TPE contributions to the amplitude, and the unpolarized differential cross section with the only elastic intermediate state is considered. The results show that the TPE corrections to the unpolarized differential cross section are about from -4% to -20% at Q²=1-1.6 GeV². After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections σ(L,T,LT,TT). We find that the TPE corrections (at Q²=1-1.6 GeV²) to σL are about from -10% to -30%, to σT are about 20%, and to σ(LT,TT) are much larger. By these analyses, we conclude that the TPE contributions in ep→enπ⁺ at small -t are important to extract the separated cross sections σ(L,T,LT,TT) and the electromagnetic form factor of π⁺ in the experimental analysis.

Keywords: differential cross section, form factor, hadronic, two-photon

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3782 Commutativity of Fractional Order Linear Time-Varying System

Authors: Salisu Ibrahim

Abstract:

The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

Procedia PDF Downloads 65
3781 Active Control Improvement of Smart Cantilever Beam by Piezoelectric Materials and On-Line Differential Artificial Neural Networks

Authors: P. Karimi, A. H. Khedmati Bazkiaei

Abstract:

The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: smart material, on-line differential artificial neural network, active control, finite element method

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3780 The Effects of Oxygen Partial Pressure to the Anti-Corrosion Layer in the Liquid Metal Coolant: A Density Functional Theory Simulation

Authors: Rui Tu, Yakui Bai, Huailin Li

Abstract:

The lead-bismuth eutectic (LBE) alloy is a promising candidate of coolant in the fast neutron reactors and accelerator-driven systems (ADS) because of its good properties, such as low melting point, high neutron yields and high thermal conductivity. Although the corrosion of the structure materials caused by the liquid metal (LM) coolant is a challenge to the safe operating of a lead-bismuth eutectic nuclear reactor. Thermodynamic theories, experiential formulas and experimental data can be used for explaining the maintenance of the protective oxide layers on stainless steels under satisfaction oxygen concentration, but the atomic scale insights of such anti-corrosion mechanisms are little known. In the present work, the first-principles calculations are carried out to study the effects of oxygen partial pressure on the formation energies of the liquid metal coolant relevant impurity defects in the anti-corrosion oxide films on the surfaces of the structure materials. These approaches reveal the microscope mechanisms of the corrosion of the structure materials, especially for the influences from the oxygen partial pressure. The results are helpful for identifying a crucial oxygen concentration for corrosion control, which can ensure the systems to be operated safely under certain temperatures.

Keywords: oxygen partial pressure, liquid metal coolant, TDDFT, anti-corrosion layer, formation energy

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3779 Finite Element Approximation of the Heat Equation under Axisymmetry Assumption

Authors: Raphael Zanella

Abstract:

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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3778 Schrödinger Equation with Position-Dependent Mass: Staggered Mass Distributions

Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

Abstract:

The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: free particle, point canonical transformation method, position-dependent mass, staggered mass distribution

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3777 Differential Diagnosis of an Asymptomatic Lesion in Contact with the Bladder

Authors: Angelis P. Barlampas

Abstract:

PURPOSE: Presentation of an interesting finding in an asymptomatic patient. MATERIAL: A patient came at hospital because of dysuric complaints and after a urologist’s prescription of a US exam of the urogenital system. The simple ultrasound examination of the lower abdomen revealed a moderate hypertrophy of the prostate and a solitary large bladder stone. The kidneys were normal. Then, the patient underwent a CT scan, which depicted the bladder stone and, as an incidental finding, a cystic lesion in contact with the upper anterior right surface of the bladder, with mural calcifications. METHOD: Abdominal ultrasound and abdominal computed tomography before and after intravenous contrast administration. RESULTS: The repeated US exam showed a cylindrical cystic lesion with a double wall and two mural hyperechoic foci, with partial posterior shadowing. Blood flow was not recognized on color doppler. The CT exam confirmed the cystic-like anechoic lesion, in the right iliac fossa, with the presence of two foci of mural calcifications. The differential diagnosis includes cases of enteric cyst, intestinal duplication cyst, chronic abscess, urachal cyst, Meckel's diverticulum, bladder diverticulum, old hematoma, thrombosed vascular aneurysm, diverticular abscess, etc. The patient refused surgical removal and is being monitored by ultrasound. CONCLUSIONS: The careful examination of the wider peri-abdominal area, especially during the routine ultrasound examination, can contribute to the identification of important asymptomatic findings. The radiologist must not be solely focused in a certain area of examination, even if the clinical doctor asks so, but should give attention to the neighboring areas, too.

Keywords: enteric cyst, US, CT, urogenital tract, miscellaneous findings

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3776 Economic Load Dispatch with Valve-Point Loading Effect by Using Differential Evolution Immunized Ant Colony Optimization Technique

Authors: Nur Azzammudin Rahmat, Ismail Musirin, Ahmad Farid Abidin

Abstract:

Economic load dispatch is performed by the utilities in order to determine the best generation level at the most feasible operating cost. In order to guarantee satisfying energy delivery to the consumer, a precise calculation of generation level is required. In order to achieve accurate and practical solution, several considerations such as prohibited operating zones, valve-point effect and ramp-rate limit need to be taken into account. However, these considerations cause the optimization to become complex and difficult to solve. This research focuses on the valve-point effect that causes ripple in the fuel-cost curve. This paper also proposes Differential Evolution Immunized Ant Colony Optimization (DEIANT) in solving economic load dispatch problem with valve-point effect. Comparative studies involving DEIANT, EP and ACO are conducted on IEEE 30-Bus RTS for performance assessments. Results indicate that DEIANT is superior to the other compared methods in terms of calculating lower operating cost and power loss.

Keywords: ant colony optimization (ACO), differential evolution (DE), differential evolution immunized ant colony optimization (DEIANT), economic load dispatch (ELD)

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3775 A Structural Equation Model of Risk Perception of Rockfall for Revisit Intention

Authors: Ya-Fen Lee, Yun-Yao Chi

Abstract:

The study aims to explore the relationship between risk perceptions of rockfall and revisit intention using a Structural Equation Modelling (SEM) analysis. A total of 573 valid questionnaires are collected from travelers to Taroko National Park, Taiwan. The findings show the majority of travellers have the medium perception of rockfall risk, and are willing to revisit the Taroko National Park. The revisit intention to Taroko National Park is influenced by hazardous preferences, willingness-to-pay, obstruction and attraction. The risk perception has an indirect effect on revisit intention through influencing willingness-to-pay. The study results can be a reference for mitigation the rockfall disaster.

Keywords: risk perception, rockfall, revisit intention, structural equation modelling

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3774 Linear fractional differential equations for second kind modified Bessel functions

Authors: Jorge Olivares, Fernando Maass, Pablo Martin

Abstract:

Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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3773 Stabilization of the Bernoulli-Euler Plate Equation: Numerical Analysis

Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

Abstract:

The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler plate equation, numerical simulations, stability, energy decay, finite difference method

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3772 Two Wheels Differential Type Odometry for Robot

Authors: Abhishek Jha, Manoj Kumar

Abstract:

This paper proposes a new type of two wheels differential type odometry to estimate the next position and orientation of mobile robots. The proposed odometry is composed for two independent wheels with respective encoders. The two wheels rotate independently, and the change is determined by the difference in the velocity of the two wheels. Angular velocities of the two wheels are measured by rotary encoders. A mathematical model is proposed for the mobile robots to precisely move towards the goal. Using measured values of the two encoders, the current displacement vector of a mobile robot is calculated by kinematics of the mathematical model. Using the displacement vector, the next position and orientation of the mobile robot are estimated by proposed odometry. Result of simulator experiment by the developed odometry is shown.

Keywords: mobile robot, odometry, unicycle, differential type, encoders, infrared range sensors, kinematic model

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